大学物理 ›› 2020, Vol. 39 ›› Issue (8): 18-20.doi: 10.16854/j.cnki.1000-0712.190527

• 教学讨论 • 上一篇    下一篇

氢原子波函数在动量表象中表示的方向问题 ———对一道典型量子力学习题求解的商榷

雷勇   

  1. 南京信息工程大学物理与光电工程学院大学物理部,江苏南京210044
  • 收稿日期:2019-11-19 修回日期:2020-01-02 出版日期:2020-08-20 发布日期:2020-09-02
  • 作者简介:雷勇( 1978—) ,男,河南南阳人,南京信息工程大学物理与光电工程学院讲师,博士,主要从事大学物理教学和宽禁带半导体功率 器件研究工作.

On the direction of hydrogen atom wave function in momentum representation

LEI Yong   

  1. Department of University Physics,Nanjing University of Information Science & Technology,Nanjing,Jiangsu 210044,China
  • Received:2019-11-19 Revised:2020-01-02 Online:2020-08-20 Published:2020-09-02

摘要:

本文探讨了周世勋先生所著《量子力学教程》中一道求氢原子电子动量概率分布的例题,对其求解中标定动量方向

的做法提出了质疑. 对求氢原子量子态的动量概率振幅而言,由于其依赖于动量方向的选取,因此标定动量方向的做法不具

有普适性. 氢原子s 态具有球对称性,其动量概率振幅中的球谐函数与动量方向无关,只有此时动量方向的标定才对概率振幅

的表示没有影响. 对求电子动量的概率分布而言,由于需要对动量的角量进行积分,因此标定动量方向是不妥的.

关键词: 氢原子波函数, 动量表象, 动量方向

Abstract: In this paper,an example of calculating the probability amplitude in momentum representation and

the probability distribution of the electron momentum in hydrogen atom in quantum mechanics course by Mr. Zhou

shixun is discussed. The method of calibration of momentum direction in the solution is questioned. For calculating

probability amplitude of momentum,the method is not universal since the representation depends on the selection of

momentum direction. Only for the s-states which have spherical symmetry and are independent of momentum direction

since the spherical harmonic function in probability amplitude is independent of momentum direction,this

method has no effect on the representation. Furthermore,for calculating the probability distribution of the electron

momentum,the calculation requires integrating the angular quantity of momentum,it is not appropriate to calibrate

the momentum direction before the calculation.

Key words: hydrogen atom, momentum representation, momentum direction